Monte Carlo simulation of two-dimensional flux-line-lattice melting

A Monte Carlo simulation of a two-dimensional flux-line-lattice (FLL) melting transition is presented. The internal energy, specific heat, Abrikosov ratio, and diffraction pattern of the magnitude ‖ψ(x)${\mathrm{\Vert }}^2$ of the order-parameter field are calculated. By examining in detail the hysteresis, histogram, and relaxation profiles of the internal energy, the existence of a first-order phase transition is concluded. Below the transition temperature ${\mathit{t}}_{\mathit{m}}$ the diffraction pattern has six sharp peaks corresponding to the hexagonal symmetry of the triangular FLL, while it shows liquidlike behavior above ${\mathit{t}}_{\mathit{m}}$. The sample-size dependence of the peak height clearly shows that the phase transition is the melting of the FLL. Comparison with earlier works is also made.